All test time adaptation methods  [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]} rely on hyper-parameters which are picked beforehand and used during the adaptation process. While we do not expect a holdout or validation set to tune adaptation parameters in the realistic test time adaptation setting, these can be used if they are available. ImageNet-C and CIFAR-10-C datasets have 4 holdout corruption sets - Spatter, speckle noise, saturate and Gaussian blur. The method can be evaluated on these holdout sets to get a reasonable indication of which range of \(\lambda \)  values which can work well in practice. For CIFAR-10-C, the best mCA of \(74.9\)  is obtained at \(\lambda =0.7\) , and remains stable for \(\sim 20\%\)  of the prior range, as shown in Figure REF . For ImageNet-C, the best mCA of \(31.8\)  is at \(\lambda =0.9\) , and the deviation from the best result at different priors (\(\lambda \) ) is shown in Figure REF . We use these prior values for the results in the paper. However, in the case of segmentation, there are no holdout sets, so we use a fixed prior \(\lambda = 0.8\)  for all datasets, even when better results were available at other \(\lambda \)  values. For example, in Figure REF , \(\lambda = 0.9\)  produces a better result for the SceneNet \(\rightarrow \)  SUN and \(\lambda =0.3\)  perform the best for SYNTHIA \(\rightarrow \)  Cityscapes, but we still report results with \(\lambda = 0.8\)  in the paper, being consistent with the spirit of test time adaptation. Further, these results demonstrate that the results are not very sensitive with respect to the exact choice of \(\lambda \) . In the future extension of this work, an algorithm can be developed to automatically find the appropriate prior weight (\(\lambda \) ) based on the test sample.
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